ArticleOriginal scientific text
Title
The vector cross product from an algebraic point of view
Authors 1
Affiliations
- Department of Statistics, University of Dortmund, Vogelpothsweg 87, D-44221 Dortmund, Germany
Abstract
The usual vector cross product of the three-dimensional Euclidian space is considered from an algebraic point of view. It is shown that many proofs, known from analytical geometry, can be distinctly simplified by using the matrix oriented approach. Moreover, by using the concept of generalized matrix inverse, we are able to facilitate the analysis of equations involving vector cross products.
Keywords
vector cross product, generalized inverse, Moore-Penrose inverse, linear equations
Bibliography
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- L.G. Chambers, A Course in Vector Analysis, Chapman and Hall, London 1969.
- B. Hague, An Introduction to Vector Analysis for Physicists and Engineers, (6th edition, revised by D. Martin), Methuen & Science Paperbacks, London 1970.
- T. Lancaster, and M. Tismenetsky, The Theory of Matrices. Academic Press, New York 1985.
- E.A. Milne, Vectorial Mechanics, Methuen & Co. Ltd., London 1965.
- C.R. Rao, and S.K. Mitra, Generalized Inverse of Matrices and its Applications, John Wiley & Sons, New York 1971.
- T.G. Room, The composition of rotations in Euclidean three-space, Amer. Math. Monthly 59 (1952), 688-692.
Pages:
67-82
Main language of publication
English
Received
1999-10-26
Accepted
2000-02-11
Published
2001
DOI: 10.7151/dmgaa.1028
Exact and natural sciences